Stable equivariant abelianization, its properties, and applications
Stable equivariant abelianization, its properties, and applications
复制标题
稳定等变阿贝尔化、其性质和应用
DOI：
10.1016/j.topol.2008.11.015
复制
发表时间：
2008
影响因子：
0.6
通讯作者：
Zhaohu Nie
中科院分区：
文献类型：
--
作者：
P. F. D. Santos;Zhaohu Nie
设G是有限群。对于基G-空间X和Mackey函子M，构造了一个拓扑Mackey函子X的稳定等变阿贝尔化.当X是基G-CW复形时，X ∈ M是G-空间意义下的无限圈空间。这给出了RO（G）-分次等变的Dold-Thom定理的一个版本。应用Elmendorf构造的一个变体，我们得到了Eilenberg-Mac Lane谱HM的模型。证明使用了Mackey函子的结构定理和我们以前的结果。
Let G be a finite group. For a based G-space X and a Mackey functor M, a topological Mackey functor X⊗˜M is constructed, which will be called the stable equivariant abelianization of X with coefficients in M. When X is a based G-CW complex, X⊗˜M is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold–Thom theorem. Applying a variant of Elmendorf's construction, we get a model for the Eilenberg–Mac Lane spectrum HM. The proof uses a structure theorem for Mackey functors and our previous results.